Is Waterfall a physical move? I guess that does actually make sense, since it's the Pokémon using its power to go against waterfalls, though the name just is kinda off-throwing, though I can't really say I agree. With the Water type HM's like Waterfall and Dive, I feel like they're just like Cut, Rock Smash, and all of those weak HM's that are just put in for progression, which you usually just teach to an HM slave. So while Dive can also be an effective way of using an AoE move without damaging your other Pokémon, it isn't really strong in itself, and most of the moves like that (Surf, Earthquake) are weak against Water type Pokémon, so it doesn't help all that much.

Yes Waterfall is a Physical move And, even if a lot of people teach Waterfall to their HM slaves, it is actually a very interesting move for strategy. The water-starter is always the water-type of my team, and as Empoleon, Blastoise and Samurott are better at Spe-Attack I teach them Surf, and I teach Waterfall to Feraligatr and Swampert (which are the two that I prefer to use in strategic battle, this is why I said Waterfall instead of Surf). For me both are the best moves for water Pokémon, and are not to neglect even their HM state can make them seem like "weak move". Notably if you want your water-type to know only one water move, at least you're sure it'll do damages and won't miss.